UPSEE Solved Model Paper 7

Given Number of molecules per unit cell, z = 4 Dimensions of unit cell a = 6.8 $\overset{0}{A}$ = 6.8 × $10^{-8}$ cm b = 4.4 $\overset{0}{A}$ × $10^{-8}$ cm c = 7.2 $\overset{0}{A}$ = 7.2 × $10^{-8}$ cm Molar mass = 21.76 We have to calculate the density (ρ) of the crystal Density of the crystal is given as: ρ = $\frac{z\times \text{Molecular weight}}{V\times \text{Avogadro Number}}$ ... (i) where, z = No of molecules per unit cell V = Volume = a × b × c Avogadro's number = 6.023 × $10^{23}$ On substituting all the values In equation (i). we get ρ = ρ = $\frac{4\times 21.76}{215.\times 10^{-22}\times 6.023\times 10^{23}}$ ρ = $\frac{87.04}{2.154\times 10^{-22}\times 6.023\times 10^{23}}$ ρ = $\frac{87.04}{129.735}$ ρ = $0.6709\,\text{gcm}^{-3}$ Hence, option 'D' is correct.